{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:46Z","timestamp":1753893826593,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The topology of the matching complex for the $2\\times n$ grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes $\\mathrm{Ind}(\\Delta_n^m)$ that include these matching complexes.\u00a0Using this matching, we determine the dimensions of the chain spaces for the resulting Morse complexes and derive bounds on the location of non-trivial homology groups for certain $\\mathrm{Ind}(\\Delta_n^m)$.\u00a0Further, we determine the Euler characteristic of $\\mathrm{Ind}(\\Delta_n^m)$ and prove that several homology groups of $\\mathrm{Ind}(\\Delta_n^m)$ are non-zero.<\/jats:p>","DOI":"10.37236\/6212","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:44:30Z","timestamp":1578671070000},"source":"Crossref","is-referenced-by-count":3,"title":["Matching and Independence Complexes Related to Small Grids"],"prefix":"10.37236","volume":"24","author":[{"given":"Benjamin","family":"Braun","sequence":"first","affiliation":[]},{"given":"Wesley K.","family":"Hough","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,10,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:44:52Z","timestamp":1579236292000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i4p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,20]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/6212","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,10,20]]},"article-number":"P4.18"}}